There's a bit more to first aid than just cleaning a wound and slapping on a band-aid. Store shelves are littered with antibiotics and antiseptics. Let's go over the differences. Image by papertygre.
Mental Floss' article covers anaesthetics rather than antibacterials, but we figured there may be more confusion between antibiotics and antibacterials. Both fall under antimicrobials, a general category of compounds that kills microbes (bacteria, fungi and other pathogens). An antibacterial is an antibiotic, but as the name implies, it can only target bacteria. Antibiotics, on the other hand, can kill or keep pathogens from growing.
Some antibiotic ointments can be used on wounds, but won't help with burns, existing infections or other, deeper pain (despite having Lidocaine, a topical analgesic). The general caveat about antibiotics also apply here: don't overuse them, as doing so could encourage bacteria to be more resistant.
Antiseptics, including hydrogen peroxide, rubbing alcohol and iodine, are mainly used to deter bacterial growth. In general, they're used to clean the skin before an injection (like during a blood test) and can be used to clean wounds. We've discussed before how hydrogen peroxide can be harsh on wounds, so if you're cleaning a reasonable wound, most experts agree that soap and water are ideal.